Need some help

I have a 93 and last week my wife was coming home from work and the battery blew up. It happened when she went to start the car. I checked the alternator and it's putting out 14.3 volts. The problem I'm having now is it has a miss every once in a while. Also when driving it feels like the engine shuts off and the check eng light comes on. Then it will go away. And the car runs fine. It's an intermittent problem. Any help on what could be going on. The day it happened it was 105 degrees. The car has 165,000 miles on it. Bill